Why chiropractors have no hospital rights?
The short answer is "because most medical doctors regard chiropractors as quacks" (or, at best, as practitioners of a technique that's unlikely to be particularly useful in a hospital setting ... and if it is needed, then it can be done just as well by DOs instead, who actually are medical doctors).
Not really: a Bill of Rights for a patient does legally oblige a hospital to follow those rights, but the document itself is not a legal document. The rights of a patient in a hospital applies to all patients in that hospital, and therefore does not have to be executed (signed by both sides of the party) as a legal document.
Interesting question... Chiropractors can work pretty much anywhere. They may have a home office, they may make house calls, they may have a completely separate office. Sometimes chiropractors will work with other health professionals. This is of course a personal choice as chiropractors have a different philosophy on how the body works from what mainstream medicine believes to be true. To answer your question chiropractors can practice almost anywhere depending on some residential zoning restrictions.